A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method

We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the r...

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Vydáno v:	Mathematical programming Ročník 163; číslo 1-2; s. 411 - 444
Hlavní autoři:	Castro, Jordi, Nasini, Stefano, Saldanha-da-Gama, Francisco
Médium:	Journal Article Publikace
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2017 Springer Nature B.V Springer Verlag
Témata:	90 Operations research, mathematical programming 90C Mathematical programming Analysis Bending machines Business administration Calculus of Variations and Optimal Control; Optimization Classificació AMS Combinatorics Costs Customers Cutting planesBenders decomposition Decomposition Efficiency Full Length Paper Humanities and Social Sciences Integer programming Interior-point methods Investigació operativa Large-scale optimization Matemàtiques i estadística Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Methods Mixed integer Mixed integer linear optimization Multi-period facility location Numerical Analysis Operations research Optimization Planning Programació matemàtica Specifications Studies Theoretical Àrees temàtiques de la UPC 90C51 Cutting planes Benders decomposition Mixed integer linear optimization 90C11 90C06 90B80 Large-scale optimization Interior-point methods Multi-period facility location
ISSN:	0025-5610, 1436-4646
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Abstract	We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 GB of) available memory in the largest instances.
AbstractList	We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 Gigabytes of) available memory in the largest instances. Peer Reviewed We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 GB of) available memory in the largest instances. We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 GB of) available memory in the largest instances.
Author	Castro, Jordi Saldanha-da-Gama, Francisco Nasini, Stefano
Author_xml	– sequence: 1 givenname: Jordi orcidid: 0000-0003-3573-4568 surname: Castro fullname: Castro, Jordi email: jordi.castro@upc.edu organization: Department of Statistics and Operations Research, Universitat Politècnica de Catalunya – sequence: 2 givenname: Stefano surname: Nasini fullname: Nasini, Stefano organization: Department of Marketing, IESEG School of Management (LEM-CNRS 9221) – sequence: 3 givenname: Francisco orcidid: 0000-0002-2074-1856 surname: Saldanha-da-Gama fullname: Saldanha-da-Gama, Francisco organization: Department of Statistics and Operations Research/Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Faculdade de Ciências, Universidade de Lisboa
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Snippet	We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this...
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SubjectTerms	90 Operations research, mathematical programming 90C Mathematical programming Analysis Bending machines Business administration Calculus of Variations and Optimal Control; Optimization Classificació AMS Combinatorics Costs Customers Cutting planesBenders decomposition Decomposition Efficiency Full Length Paper Humanities and Social Sciences Integer programming Interior-point methods Investigació operativa Large-scale optimization Matemàtiques i estadística Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Methods Mixed integer Mixed integer linear optimization Multi-period facility location Numerical Analysis Operations research Optimization Planning Programació matemàtica Specifications Studies Theoretical Àrees temàtiques de la UPC
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Title	A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method
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